MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Let X be a random variable with mean 6 and variance 3. Let Y be the random variable
counting the number of times the number 1 appears when rolling six fair four-sided dice.
Assume that X and Y are independent. Define Z to be the random variable 2X − 3Y + 1.
Find E(Z). 

Expert Solution
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Step 1

Given that 

E(X) = 6 , V(X) = 3

Let Y be the random variable
counting the number of times the number 1 appears when rolling six fair four-sided dice.

p = 1/4 = 0.25 , n =6 , q =1 - p =1 - (1/4) =3/4 =0.75

p=Probability of the number of times the number 1

Y = The number of times the number 1

Y ~ Binomial (n = 6 , p = 0.25)

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